1. Field of the invention
The present invention relates to lenses used in optical systems and, more particularly to a new lens or a new lens group. It also relates to a linear spectrometer based on such a lens or lens group.
2. Description of the Prior Art
A spectrometer generally uses a diffraction grating to spread the spectral components of incident light on a one-dimensional detector. The detector is usually composed of pixels linearly distributed along a line. However, the diffracted light is not spread linearly on the detector, which means that the wavelength on pixel 1 is not linearly correlated with the wavelength on the pixel 2, and so on from pixel to pixel. The resolution is therefore not constant for all the spectral range of the spectrometer. To know which pixel corresponds to which wavelength, a complex calibration process must be applied very carefully to prevent errors.
It would thus be desirable to have an optical system that would yield a linear output when used with a diffraction grating, thereby substantially eliminating a time consuming calibration process. This optical system would introduce the desirable amount of distortion to obtain a linear relation between pixel position and wavelength.
Introducing the desired amount of distortion in an optical system is possible and relatively straight forward for optical designers. For example, known fxcex8 lenses (as in U.S. Pat. No. 4,695,132 issued on Sep. 22, 1987 to Sakuma and No. 4,770,517 issued on Sep. 13, 1988 also to Sakuma) used in laser scanner systems are one of the most popular lenses using distortion to get a linear output plane. In this case, the linearity is related to the scanning angle.
The height of the image position in a single element optical system is proportional to the tangent of the incident angle on the optical system. In order to have linearity with the wavelength, the optical system when used with a diffraction grating must introduce distortion in such a way that the relation of the height of the image respects the relation A f sin(xcex8), where A is a constant, f is the focal length of the optical system and xcex8 the angle of incidence. This condition is described in co-pending U.S. application Ser. No. 09/406,576 of Sep. 24, 1999, assigned to the same assignee.
This technique is more powerful than the one proposed in U.S. Pat. No. 4,786,174 issued on Nov. 22, 1988. In the arrangement proposed in the latter patent, an optimal linearity of the wavelength scale on the plane of detector can be achieved. We suggest a technique to obtain exact linearity of the wavelength scale on the plane of detector. The level of error is fixed by the designer during the design process.
Accordingly, it is an object of the present invention to provide a new and improved spectrometer.
It is also an aim of the present invention to provide a spectrometer which combines simultaneously the f sin(xcex8) characteristic for obtaining a linear scale of the wavelength on the image plane and a well-corrected image plane for each spectral component.
The present invention therefore provides a linear spectrometer for spectrally measuring an optical signal. The spectrometer includes an input for receiving the optical signal along an optical axis, and a diffraction grating for separating the received optical signal into spectral components thereof, each spectral component being diffracted at a diffraction angle xcex8 from the optical axis. An optical correcting element having an effective focal length f is provided, this optical correcting element focusing the spectral components on an image plane in accordance with an f sin(xcex8) distribution. Detecting means are further provided for detecting the spectral components in the image plane.
If an f-sin(xcex8) lens or lens group is introduced for instance in a spectrometer, this new lens provides a correction for the deflection of the laser beam which takes place at a linear position with the wavelength in the detector plane. Specifically, when the diffraction grating is positioned on the entrance pupil of the f-sin(xcex8) lens having an effective focal length of f, with respect to the optical axis thereof, the beam will be focused onto the detector plane at a point which is displaced by a distance of f-sin(xcex8) from the optical axis. According to the grating equation at normal incidence             sin      ⁡              (        θ        )              =                  m        ·        λ                    n        ·        Λ              ,
where xcex8 is the diffraction angle, m is the diffraction order, xcex is the wavelength, n the index of the refraction and xcex9 the grating period, the distance from the optical axis of the focused beam is a linear function of the wavelength. Then the calibration can be simplified because the spectral component of a light signal spread on the detector is linearly distributed on the linear detector. Furthermore, the resolution is constant over the wavelength operating range. The designation xe2x80x9cf sin(xcex8) lensxe2x80x9d, or xe2x80x9cf-xcex lensxe2x80x9d, is derived from such a fact.
The present invention can solve the problem associated with the non-linear imaging process in the spectrometer and it can also solve other problems. This invention is intended to provide a new lens or lens group which can be used with a diffraction grating to provide a linear output plane with the wavelength (xcex), but also with the order of diffraction (m), or with the grating spatial frequency (1/xcex9), or with the inverse of the index of refraction (n).
Accordingly, the invention provides a new lens or a new lens group with the proper amount of distortion to provide an f-Sin(xcex8) characteristic. The optical lens or lens group of the present invention has a positive or a negative power and it can be refractive, diffractive and reflective or a combination of all these properties.